Answer:
see explanation
Step-by-step explanation:
The slope m of the line = tan45° = 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 1 , then
y = x + c
To find c substitute (2, 1 ) into the equation
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = x - 1 ← equation of line
When x = 0 then y = 0 - 1 = - 1
The line passes through (0, - 1 )
Please help
Which expression is equivalent to (3w-8)-4(2w+3)?
A. 11w+4
B. -5w-5
C. -5w+4
D. -5w-20
Answer:
-5w-20 is equivalent to (3w-8)-4 (2w+3)
40 points and brainliest to the best correct answer, questions in photo.
Please do and explain numbers 2, 4, 6, and 8, thank you.
Answer:
2. w = -3
4. c = -2
6. r = 7
8. n = 4
Step-by-step explanation:
It's hard to read the photo, but I'll try.
2.
[tex] 2^{w + 4} \times 2^{4w + 6} = 2^{2w + 1} [/tex]
On the left side, you have a product of 2 powers with the same base.
Give the same base and add the exponents, as in the rule
[tex] a^m \times a^n = a^{m + n} [/tex]
You get on the left side 2 to the sum of the exponents.
[tex] 2^{w + 4 + 4w + 6} = 2^{2w + 1} [/tex]
Simplify the long exponent on the left side.
[tex] 2^{5w + 10} = 2^{2w + 1} [/tex]
Now we have another rule we can use. If two powers are equal, and their bases are equal, then the exponents must be equal.
Here, 2 to the power 5w + 10 equals 2 to the power 2w + 1. Since both bases are 2 and are equal, then the exponents must be equal.
5w + 10 = 2w + 1
Subtract 2w from both sides. Subtract 10 from both sides.
3w = -9
Divide both sides by 3.
w = -3
4.
[tex] \dfrac{1}{5} = 5^{2c + 3} [/tex]
We need to write the left side as a power of 5. Then we equate the exponents like we did in problem 2.
Recall the rule:
[tex] a^{-n} = \dfrac{1}{n} [/tex]
Apply this rule to the left side in reverse.
[tex] 5^{-1} = 5^{2c + 3} [/tex]
Now we have two powers that are equal, both having the same base, 5, so the exponents must be equal.
2c + 3 = -1
2c = -4
c = -2
6.
[tex] 216 = 6^{2r - 11} [/tex]
This is the same idea as problem 4. Write the left side as a power of 6.
[tex] 6^3 = 6^{2r - 11} [/tex]
[tex] 2r - 11 = 3 [/tex]
[tex] 2r = 14 [/tex]
[tex] r = 7 [/tex]
r = 7
8.
[tex] 4^{n} \times 4^{2n - 9} = 64 [/tex]
This problem is similar to problem 2.
[tex] 4^{n + 2n - 9} = 4^3 [/tex]
[tex] 4^{3n - 9} = 4^3 [/tex]
3n - 9 = 3
3n = 12
n = 4
Tamara says she used the GCF to factor the expression 21x 56xy as 7(3x 8xy). Is she correct? Explain.
7x is the GCF of the polynomial.
PolynomialPolynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Given
21x + 56xy is a polynomial.
To findThe GCF to factor the polynomial.
How to find the GCF to factor the polynomial?21x + 56xy is a polynomial.
Take 7x common from the polynomial. we have
21x + 56xy
7x (7 + 8y)
Thus, 7x is the GCF of the polynomial.
More about the polynomial link is given below.
https://brainly.com/question/17822016
9. What type of transformation is shown?
Select all that apply.
A. A reflection
C. a rigid motion
B. A translation
D. a turn
HELPPPP !!! What is the value of x in trapezoid ABCD?
O xE15
O X20
O X=45
O x=60
How do you solve for x in the equation 3(x squared-8x) = 0
[tex]3(x^2-8x)=0\implies x^2-8x=\cfrac{0}{3}\implies x^2-8x=0 \\\\\\ \stackrel{\textit{common~factoring}}{x(x-8)=0} \implies \begin{cases} \boxed{x=0}\\[-0.5em] \hrulefill\\ x-8=0\\ \boxed{x=8} \end{cases}[/tex]
PLEASE CAN SOMEONE HELP ASAP!!!!!!!!
DUE BY 11:59 OMGGG
Answer:
A, C, F
Step-by-step explanation:
JK is proportional to PQ, so that would be 8/x. Then, JL is proportional to PR, which would be 10/5. So, the answer is: 8/x = 10/5
Then, C would also be correct as KL is proportional to QR, and JK is proportional to PQ.
Finally, F is correct as JK to KL is proportional to PQ to QR, as JK is proportional to PQ, and KL is proportional to QR.
Slove each inequality and graph it’s solution. (the sign has a line under it but I can’t do it on my keyboard)
|5a| > 10
if you are picking a number between 1-20 what is the probability that you will pick an even numder or a multiple of three
Answer:
The probability of an event happening is desired outcome/sample space.
For our sample space, it’s just the number of numbers: 20.
The outcome you want has some overlap: 6. 12. 18. So, we’ll subtract these as they fit both criteria.
Even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (10 numbers)
Multiples of 3: 3, 6, 9, 12, 15, 18 (6 numbers)
Pr(A or B) = Pr(A) + Pr(B) - Pr(overlap, also known as A intersect B)
Pr(even or mult. of 3) = 10/20 + 6/20 - 3/20 (the overlap)
= 13/20.
So, there is a 65% of you picking an even number or a multiple of three.
Step-by-step explanation:
Hopes this helps. <3
can someone help i don't understand this
What is the volume of the cube??
Answer:
125 inches cubed
Step-by-step explanation:
volume= height*width*length
5*5*5=125
A, B and C lie on a straight line.
Given that angle
y
= 128° and angle
z
= 91°, work out
x
.
Answer:
y+what ever the angle inside=180 since its on a line
180-128=52
52+z+x=180since thats always the angles of a triangle added up
52+91+x=180
add
143+x=180
-143
x=37
Hope This Helps!!!
Which is the answer?
A: 19, 95, 114; obtuse
B: 10, 50, 60; acute
C: 16, 80, 96; obtuse
D: 12, 60, 72; acute
E: 15, 75, 90; right
15, 75, 90; right
===================================================
Explanation:
The ratio 1:5:6 scales up to x:5x:6x for some positive real number x.
The three interior angles are x, 5x and 6x. For any triangle, the interior angles always add to 180.
x+5x+6x = 180
12x = 180
x = 180/12
x = 15
So,
5x = 5*15 = 756x = 6*15 = 90The triangle has angles of 15, 75 and 90 degrees.
Because we have a 90 degree angle, this is a right triangle.
Note how 15+75+90 = 180 to help confirm the answer.
Question 3
In the diagram, m ll n. Identify all of the angles that are congruent to <2.
A. <3, <6, <7
B. <1, <7, <8
C. <1, <3, <4
D. <4, <6, <8
7) When Ernest Rutherford worked with radioactive decay of radium, he noticed it had a
half-life of 100 days. This means that whatever the amount of radium he has at the
beginning, in 100 days he'll have half of that amount. In one experiment, he starts with
320 mg of radium, and stores it for 40 days. How much radium will be left after the 40
days?
Using an exponential function, it is found that 242.5 mg of radium will be left after the 40 days.
What is an exponential function?The exponential function for the amount of a decaying substance is modeled by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which:
A(0) is the initial amount.k is the decay rate, as a decimal.In this problem, the half-life is of 100 days, hence:
[tex]A(100) = 0.5A(0)[/tex]
Which is used to find k.
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.5A(0) = A(0)e^{-100k}[/tex]
[tex]e^{-100k} = 0.5[/tex]
[tex]\ln{e^{-100k}} = \ln{0.5}[/tex]
[tex]-100k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{100}[/tex]
[tex]k = 0.0069314718[/tex]
Then, the equation is:
[tex]A(t) = A(0)e^{-0.0069314718t}[/tex]
He started with 320 mg of radium, hence [tex]A(0) = 320[/tex], and the equation is:
[tex]A(t) = 320e^{-0.0069314718t}[/tex]
After 40 days, the amount left is:
[tex]A(40) = 320e^{-0.0069314718(40)} = 242.5[/tex]
242.5 mg of radium will be left after the 40 days.
You can learn more about exponential functions at https://brainly.com/question/25537936
The group is trying to determine what the price difference would be per passenger if 10 of them go on the trip versus if 16 of them go on the trip. What is the difference in price per passenger for a group of 16 versus a group of 10? $46. 25 $36. 25 $56. 25 $26. 25.
The difference in price per passenger for a group of 16 versus a group of 10 is $26.25.
Given
A group of friends chartered a deep-sea fishing boat out of Destin, FL.
The graph below represents the total cost, in dollars, of the trip as a function of the number of people going.
The group is trying to determine what the price difference would be per passenger if 10 of them go on the trip versus if 16 of them go on the trip.
What is a linear equation?An equation between two variables that gives a straight line when plotted on a graph.
The group of 16 people would cost $2,500, so it would be $156.25 for each person.
The group of 10 people would cost 1,300 (I got this from going to 10 on the chart then following it up to the line), so it would be $130 per person.
Then, $156.25 - $130 = $26.25
Hence, the difference in price per passenger for a group of 16 versus a group of 10 is $26.25.
To know more about the Linear equation click the link given below.
https://brainly.com/question/13553275
Function or not a function
Answer:
Not a function.
Step-by-step explanation:
Due to the fact that an element from the first set of components is associated with one and only one element from the other. In this case, as it is a circumference, the elements match with more than one element of the other set. I'll give you an example.
Note: I've tried to keep it as simple as possible, and I'm not natively English so I don't really know how some things are mentioned, but I've also made a picture representation and I think it simplifies.
Natalie bought 10 pizzas for a party. When the party was over, she noticed 1/5 of the
pizza was gone. How much pizza did everyone eat at the party?
Answer:
8 pizzas
Step-by-step explanation:
If 1/5 was remaining, the hoard consumed 4/5 of all the pizza.
(4/5)*(10 pizzas) = 8 pizzas
Answer:
2 pizzas
Step-by-step explanation:
[tex]\frac{10}{1}[/tex]*[tex]\frac{1}{5}[/tex]=[tex]\frac{10}{5}[/tex]
then divided 5 by 10 and it equals 2 pizzas.
find the sum of difference
What is the difference of the polynomials?
-
(12x^2–11y^2 - 13x)-(5x^2 – 14y^2 –9x )
-
O 7x2 + 3y2 - 4x
O 7X2 - 3y2 - 4x
O 7x2 - 25y2-22x
O 17X2 - 25y2 - 22x
Answer:
O 7x2 + 3y2 - 4x
.........
[tex]\qquad \qquad\huge \underline{\boxed{\sf ᴀɴsweʀ}}[/tex]
The Correct choice is ~ A
[tex]\qquad \sf \dashrightarrow \: 7 {x}^{2} + 3 {y}^{2} - 4x[/tex]
[tex]\large \boxed{ \mathrm{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
[tex]\sf \dashrightarrow \:(12 {x}^{2} - 11y { }^{2} - 13x) - (5 {x}^{2} - 14y { }^{2} - 9x)[/tex]
[tex]\sf \dashrightarrow \:12 {x}^{2} - 11y { }^{2} - 13x- 5 {x}^{2} + 14y { }^{2} + 9x[/tex]
[tex] \sf \dashrightarrow \: 12 {x}^{2} - 5 {x}^{2} - 11y { }^{2} + 14 {y}^{2} - 13x + 9 [/tex]
[tex]\sf \dashrightarrow \: 7 {x}^{2} + 3 {y}^{2} - 4x[/tex]
clarissa earned 8$ for working 3 hours. how many hours will she have to work to earn 16$
Answer:
6 hours you're welcome owo
HELP WITH THIS PLEASE
Step-by-step explanation:
1a.
[tex](2 {p}^{2} )^{3} = {2}^{3} {p}^{6} = 2p \times 2p\times 2p\times p\times p\times p[/tex]
(2p^2)^3 without exponents will represent 2p being multiplied by 2p 2 times and by p 3 times.
1b. Solve:
Include exponent outside parenthese:
[tex]{2}^{3} {p}^{2 \times 3} [/tex]
[tex]8 {p}^{6} [/tex]
8p^6 is your answer for part B.
mark's age, x , is 6 times his age 2 years ago. which equation represents the statement?
Answer:
x = 6(x - 2)
Step-by-step explanation:
His age now is x.
His age 2 years ago was x - 2.
x = 6(x - 2)
One-Step Equations pls help 30 points if you solve them
Answer:
No1.
let x represent number of ice cream cones
80=12+4x
80-12=4x
68=4x
x=68/4
x=17
Check:
12+4(17)
=12 +68=80
3. 5x+14=9
collect like terms
5x=9-14
5x=-5
x=-5/5
x= -1
check:
5(-1)+14= -5+14 =9
Complete the statements to solve for x. By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN. Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x 4 EndFraction. Cross-multiply: (x – 5)( ) = x(x – 3). Distribute: x(x) x(4) – 5(x) – 5(4) = x(x) x(–3). Multiply and simplify: x2 – x – = x2 – 3x. Solve for x: x =.
The value of x is 10.
GivenBy the converse of the side-splitter theorem;
If [tex]\rm \dfrac{JK}{KL}[/tex] then, KM||JN.
What is the side-splitter theorem?If a line is parallel to one side of the triangle and intersects the other 2 sides, it divides the sides proportionally.
If a line is drawn parallel to one side of the triangle, then it divides the other two sides in the same ratio.
KM || JN
[tex]\rm \dfrac{JK}{KL}= \dfrac{NM}{ML}\\\\[/tex]
Where JK = x-5, KL = x-3, NM = x, and KL = x+4.
Substitute all the values in the equation
[tex]\rm \dfrac{JK}{KL}= \dfrac{NM}{ML}\\\\ \dfrac{x-5}{x-3} = \dfrac{x}{x+4}\\\\(x-5) (x+4) = x(x-3)\\\\x^2+4x-5x-20 = x^2-3x\\\\x^2-x-20-x^2+3x=0\\\\2x-20=0\\\\2x = 20\\\\x = \dfrac{20}{2}\\\\x=10[/tex]
Hence, the value of x is 10.
To know more about the side-splitter theorem click the link given below.
https://brainly.com/question/10612748
Answer:
NM/ML
x+4
20
10
Step-by-step explanation:
just did it
-edge 2022
The area of a circular swimming pool is approximately 18m2. What is the best estimate for the radius?
Answer:
Below
Step-by-step explanation:
Since S = πr², then r=√{S/π)=2.3942
NEED THIS NOW.
Three years ago, Jolene bought $750 worth of stock in a software company. Since then the value of her purchase has been increasing at an average rate of 12
1
2
% per year. How much is the stock worth now? (Round each money calculation you make to the nearest cent.)
Answer:
1053.7$
Step-by-step explanation:
750$ x 12%= 90
first year: 750 + 90 = 840
840$ x 12%= 100.8$
second year: 840+ 100.8= 940.8
940.8$ x 12%= 112.896
third year (now)= 940.8+ 112.896 = 1053.696$
What is the slope of the line
I will show the options, for example how I wish it to be is like, "1 Acute" something like that, I will show you the answers.
Acute
Isosceles
Obtuse
Answer:
1. Acute
2. Obtuse
3. Isosceles
There are 102 coins with the value of 17.10$ and they are quarters and dimes, how many of the coins are dimes
Answer:
Let x = number of dimes
y = number of quarters
Equation 1 is then x + y = 100, that one is easy.
Now you have to worry about values of each, and since a dime is $0.10 and a quarter is $0.25, that means that the number of each times their respective dollar amounts has to add up to the total dollar amount.
Equation 2 is then 0.1x + 0.25y = 14.05
To rewrite for clarity you have:
x + y = 100 (1)
0.1x + 0.25y = 14.05 (2)
Now you can solve this any number of ways, I'm going to use addition by multiplying both sides of equation 1 by -1/10 and then adding it to equation 2.
-0.1x - 0.1y = -10
0.1x + 0.25y = 14.05
0.15y = 4.05
don't let the decimals trip you up, that's the same as
15y = 405
y = 27 quarters
Now use that value in the original equation 1 to get
x = 100 - 27 = 73 dimes
To check use the values in the equation 2
$0.1*(73) + $0.25*(27) = $14.05
$7.30 + $6.75 = $14.05
